Heat transfer in laminar flow microtube is numerically explored with an objective of discriminating conjugate heat transfer process experienced in a microtube under two different thermal conditions. Two classical thermal conditions – constant heat flux and constant wall temperature – are imposed separately on the outer surface of a microtube. Wide parametric variations are considered in this study, for the two thermal conditions, albeit the problem under consideration being very classical from both geometry and thermal condition point of view. The parametric variations considered in this work include wall thickness, wall conductivity and coolant flow rate. An expression for Nusselt number in terms of radial (or transverse) and axial conduction number is presented and validated against existing theoretical correlation as well as reported experimental data for both circular and non-circular channels. Dominance of axial conduction over radial (or transverse) conduction is explored and it is found that the effect of wall material on conjugate heat transfer plays an important role. Additionally, it is also observed that with the increase in coolant flow rate, the ratio of radial to axial conduction number increases for both thermal boundary conditions. © 2019, Indian Academy of Sciences.